4. (Based on # 7 from PE07.) A husband and wife have a health insurance policy t

Question

4. (Based on # 7 from PE07.) A husband and wife have a health insurance policy that reimburses their combined annual covered health expense. The annual covered heath expense for the husband is X and for the wife it is Y. You are given: I. X and Y are independent. IL. X is uniform on (0,5). III. Y is uniform on (0,7). insurance payment covers the combined annual expenses of husband and wife, subject only to an annual payment limit of 10. Find the expected annual insurance payment P (rounded). (A) P=4 (B) P=5 (C) P=6 (D) P=7 (E) P=8

Explanation / Answer

The mean and variances of sum of two normal distirbutions is equal to the sum of the two means and variances respectively.

The mean for husband =(lower limit+higherlimit)/2 =0+5/2=2.5

The mean for wife=(lower limit+higher limit)/2 =0+7/2=3.5

The combined mean =2.5+3.5=6

Thus the expected annual payment P will be 6. (sum of means of husband and wife

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